navier_stokes_taylor_error_dg.cc

The Navier-Stokes equations for the Taylor benchmark – error analysis

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "taylor_exact.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
Float err_u_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
Float err_p_linf_expected = (argc > 2) ? atof(argv[2]) : err_u_linf_expected;
bool have_kinetic_energy = (argc > 3);
bool dump = (argc > 4);
Float Re;
field uh;
din >> catchmark("Re") >> Re
>> catchmark("u") >> uh;
space Xh = uh.get_space();
size_t k = Xh.degree();
geo omega = Xh.get_geo();
string approx = "P"+itos(k)+"d";
space Qh (omega, approx);
field ph(Qh);
din >> catchmark("p") >> ph;
size_t d = omega.dimension();
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(2*k+1);
#ifdef TODO
Float p_moy = integrate (omega, ph, iopt);
ph = ph-p_moy;
#else // TODO
trial p (Qh); test q (Qh);
form mp = integrate(p*q);
Float p_moy = mp (ph, field(Qh,1));
ph = ph-p_moy;
#endif // TODO
string high_approx = "P"+itos(k+1)+"d";
space Xh1 (omega, high_approx, "vector"),
Qh1 (omega, high_approx);
field euh = interpolate (Xh1, uh-u_exact());
field eph = interpolate (Qh1, ph-p_exact(Re,have_kinetic_energy));
Float err_u_l2 = sqrt(integrate (omega, norm2(uh-u_exact()), iopt));
Float err_u_linf = euh.max_abs();
Float err_u_h1 = sqrt(integrate (omega, norm2(grad_h(euh)), iopt)
+ integrate (omega.sides(), (1/h_local())*norm2(jump(euh)), iopt));
Float err_p_l2 = sqrt(integrate (omega, sqr(ph-p_exact(Re,have_kinetic_energy)), iopt));
Float err_p_linf = eph.max_abs();
derr << "err_u_l2 = " << err_u_l2 << endl
<< "err_u_linf = " << err_u_linf << endl
<< "err_u_h1 = " << err_u_h1 << endl
<< "err_p_l2 = " << err_p_l2 << endl
<< "err_p_linf = " << err_p_linf << endl;
if (dump) {
dout << catchmark("uh") << uh
<< catchmark("u") << interpolate (Xh, u_exact())
<< catchmark("eu") << euh
<< catchmark("ph") << ph
<< catchmark("p") << interpolate (Qh, p_exact(Re,have_kinetic_energy))
<< catchmark("ep") << eph;
}
return ((err_u_linf <= err_u_linf_expected) && (err_p_linf <= err_p_linf_expected)) ? 0 : 1;
}
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
rheolef::integrate_option::gauss
@ gauss
Definition: integrate_option.h:132
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::field
field_basic< Float > field
see the field page for the full documentation
Definition: field.h:419
rheolef::derr
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
dump
verbose clean transpose logscale grid shrink ball stereo iso volume skipvtk deformation fastfieldload lattice reader_on_stdin color format format format format format format format format format format format format format format format format format format dump
Definition: iorheo-members.h:119
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
main
int main(int argc, char **argv)
Definition: navier_stokes_taylor_error_dg.cc:29
rheolef.h
rheolef - reference manual
p_exact
Definition: taylor_exact.h:27
p
Definition: sphere.icc:25
taylor_exact.h
The Taylor benchmark – the exact solution of the Stokes problem.
u_exact
g u_exact
Definition: taylor_exact.h:26